Download or read book Double jump Diffusion Model for VIX written by Xin Zang and published by . This book was released on 2016 with total page 38 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper studies the continuous-time dynamics of VIX with stochastic volatility and jumps in VIX and volatility. Built on the general parametric affine model with stochastic volatility and jumps in the logarithm of VIX, we derive a linear relationship between the stochastic volatility factor and the VVIX index. We detect the existence of a co-jump of VIX and VVIX and put forward a double-jump stochastic volatility model for VIX through its joint property with VVIX. Using the VVIX index as a proxy for stochastic volatility, we use the MCMC method to estimate the dynamics of VIX. Comparing nested models of VIX, we show that the jump in VIX and the volatility factor are statistically significant. The jump intensity is also stochastic. We analyze the impact of the jump factor on VIX dynamics.
Download or read book Pricing Models of Volatility Products and Exotic Variance Derivatives written by Yue Kuen Kwok and published by CRC Press. This book was released on 2022-05-08 with total page 283 pages. Available in PDF, EPUB and Kindle. Book excerpt: Pricing Models of Volatility Products and Exotic Variance Derivatives summarizes most of the recent research results in pricing models of derivatives on discrete realized variance and VIX. The book begins with the presentation of volatility trading and uses of variance derivatives. It then moves on to discuss the robust replication strategy of variance swaps using portfolio of options, which is one of the major milestones in pricing theory of variance derivatives. The replication procedure provides the theoretical foundation of the construction of VIX. This book provides sound arguments for formulating the pricing models of variance derivatives and establishes formal proofs of various technical results. Illustrative numerical examples are included to show accuracy and effectiveness of analytic and approximation methods. Features Useful for practitioners and quants in the financial industry who need to make choices between various pricing models of variance derivatives Fabulous resource for researchers interested in pricing and hedging issues of variance derivatives and VIX products Can be used as a university textbook in a topic course on pricing variance derivatives
Download or read book Some Stability Results of Parameter Identification in a Jump Diffusion Model written by Dana Düvelmeyer and published by . This book was released on 2005 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book A Note on Uniqueness of Parameter Identification in a Jump Diffusion Model written by Hans-Jörg Starkloff and published by . This book was released on 2005 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Financial Mathematics Volatility and Covariance Modelling written by Julien Chevallier and published by Routledge. This book was released on 2019-06-28 with total page 381 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an up-to-date series of advanced chapters on applied financial econometric techniques pertaining the various fields of commodities finance, mathematics & stochastics, international macroeconomics and financial econometrics. Financial Mathematics, Volatility and Covariance Modelling: Volume 2 provides a key repository on the current state of knowledge, the latest debates and recent literature on financial mathematics, volatility and covariance modelling. The first section is devoted to mathematical finance, stochastic modelling and control optimization. Chapters explore the recent financial crisis, the increase of uncertainty and volatility, and propose an alternative approach to deal with these issues. The second section covers financial volatility and covariance modelling and explores proposals for dealing with recent developments in financial econometrics This book will be useful to students and researchers in applied econometrics; academics and students seeking convenient access to an unfamiliar area. It will also be of great interest established researchers seeking a single repository on the current state of knowledge, current debates and relevant literature.
Download or read book Jump Diffusion Process written by and published by . This book was released on with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book General Equilibrium Option Pricing Method Theoretical and Empirical Study written by Jian Chen and published by Springer. This book was released on 2018-04-10 with total page 163 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book mainly addresses the general equilibrium asset pricing method in two aspects: option pricing and variance risk premium. First, volatility smile and smirk is the famous puzzle in option pricing. Different from no arbitrage method, this book applies the general equilibrium approach in explaining the puzzle. In the presence of jump, investors impose more weights on the jump risk than the volatility risk, and as a result, investors require more jump risk premium which generates a pronounced volatility smirk. Second, based on the general equilibrium framework, this book proposes variance risk premium and empirically tests its predictive power for international stock market returns.
Download or read book Option Valuation Under Stochastic Volatility II written by Alan L. Lewis and published by . This book was released on 2016-05-12 with total page 748 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a sequel to the author's well-received "Option Valuation under Stochastic Volatility." It extends that work to jump-diffusions and many related topics in quantitative finance. Topics include spectral theory for jump-diffusions, boundary behavior for short-term interest rate models, modelling VIX options, inference theory, discrete dividends, and more. It provides approximately 750 pages of original research in 26 chapters, with 165 illustrations, Mathematica, and some C/C++ codes. The first 12 chapters (550 pages) are completely new. Also included are reprints of selected previous publications of the author for convenient reference. The book should interest both researchers and quantitatively-oriented investors and traders. First 12 chapters: Slow Reflection, Jump-Returns, & Short-term Interest Rates Spectral Theory for Jump-diffusions Joint Time Series Modelling of SPX and VIX Modelling VIX Options (and Futures) under Stochastic Volatility Stochastic Volatility as a Hidden Markov Model Continuous-time Inference: Mathematical Methods and Worked Examples A Closer Look at the Square-root and 3/2-model A Closer Look at the SABR Model Back to Basics: An Update on the Discrete Dividend Problem PDE Numerics without the Pain Exact Solution to Double Barrier Problems under a Class of Processes Advanced Smile Asymptotics: Geometry, Geodesics, and All That
Download or read book Two Simple Jump Diffusion Models With a Simple Estimation written by Marek Kolman and published by . This book was released on 2020 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Two simple but practical jump diffusion models are presented. It turns out that the stock returns these model generate, lead to return densities that are Gaussian mixture densities which results into a simple estimation using historical returns data. The first model uses up/down jumps of constant jump sizes, the second model uses normally-distributed jumps.
Download or read book Perpetual Barrier Options in Jump diffusion Models written by Pavel V. Gapeev and published by . This book was released on 2006 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Jump Diffusion Calibration Using Differential Evolution written by David Ardia and published by . This book was released on 2017 with total page 6 pages. Available in PDF, EPUB and Kindle. Book excerpt: The estimation of a jump-diffusion model via Differential Evolution is presented. Finding the maximum likelihood estimator for such processes is a tedious task due to the multimodality of the likelihood function. The performance of the Differential Evolution algorithm is compared with standard optimization techniques.
Download or read book Efficient Hedging for a Complete Jump Diffusion Model written by Michael Kirch and published by . This book was released on 2002 with total page 16 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Ein Jump Diffusion Libor Modell und Dessen Kalibrierung Auf Caplets written by Alexander Heidebrecht and published by . This book was released on 2014 with total page 75 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book A Jump diffusion Libor Model and Its Robust Calibration written by Denis Belomestny and published by . This book was released on 2006 with total page 30 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Parameters Estimation for Jump diffusion Process Based on Low and High Frequency Data written by Cai Zhu and published by . This book was released on 2011 with total page 94 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Exact Simulation of Jump diffusions written by Dmitry Smelov and published by . This book was released on 2014 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis treats the problems of exact simulation and parameter inference for jump-diffusion processes. It has two parts. The first part develops a method for the exact simulation of a skeleton, a hitting time and other functionals of a one-dimensional jump-diffusion with state-dependent drift, volatility, jump intensity and jump size. The method requires the drift function to be C1, the volatility function to be C2, and the jump intensity function to be locally bounded. No further structure is imposed on these functions. The method leads to unbiased simulation estimators of security prices, transition densities, hitting probabilities, and other quantities. Numerical results illustrate its features. The second part develops and analyzes likelihood estimators for the parameters of a discretely-observed jump diffusion. We consider the case when the transition density of the process admits an expansion in terms of an infinite series. A randomization technique leads to an unbiased Monte Carlo estimator of the transition density and the likelihood function. We provide conditions under which resulting likelihood estimators are consistent and asymptotically normal. The method avoids the second-order bias of conventional discretization-based estimators. Unlike the estimators based directly on the density expansion, we do not require high-frequency observations. Numerical results confirm the method's properties.
Download or read book Option Valuation Under Stochastic Volatility written by Alan L. Lewis and published by . This book was released on 2000 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt:
